AP ICET 2014

Question 103

The area of a rectangular metal sheet is 60 sq.m. The sum of its length and diagonal is equal to 5 times its breadth, Then the difference (in metres) between length and breadth is

Solution

Let the length , breadth, diagonal length be l, b and d respectively.
We know that d = $$\sqrt{\ l^2+b^2}$$

We are given that : 
$$l+\sqrt{\ l^2+b^2}\ =\ 5\cdot b$$
$$\sqrt{\ l^2+b^2}\ =\ 5\cdot b-l$$
Squaring both sides and then putting l*b = 60 (given in question), we get:
$$b^2=25b^2-600$$
$$b=5$$
Hence, l = 12 and difference in length and breadth = 7 


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